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Constant angle surfaces in ${ℍ}^{2}×ℝ$. (English) Zbl 1173.53012
Let ${H}^{2}×ℝ$ be the Riemannian product of a two-dimensional real hyperbolic plane with constant sectional curvature $-1$ and a Euclidean line. The authors classify all surfaces in ${H}^{2}×ℝ$ for which the angle between the normal spaces of the surface and the Euclidean line $ℝ$ in the product is constant.

##### MSC:
 53B25 Local submanifolds
##### Keywords:
surfaces; real hyperbolic plane; product manifold
##### References:
 [1] P. Cermelli and A.J. Di Scala. Constant-angle surfaces in liquid crystals. Philosophical Magazine, 87(12) (2007), 1871–1888. · doi:10.1080/14786430601110364 [2] F. Dillen, J. Fastenakels, J. Van der Veken and L. Vrancken. Constant Angle Surfaces in S 2 $×$ $ℝ$. Monaths. Math., 152(2) (2007), 89–96. · Zbl 1140.53006 · doi:10.1007/s00605-007-0461-9 [3] F. Dillen and M.I. Munteanu. Surfaces in $ℍ$ 2 $×$ $ℝ$. Pure and Applied Differential Geometry, PADGE 2007, Berichte aus der Mathematik (Shaker Verlag) Eds. Franki Dillen, Ignace Van de Woestyne, 185–193. [4] J. Fastenakels, M.I. Munteanu and J. Van der Veken. Constant angle surfaces in the Heisenberg group, preprint. [5] M.I. Munteanu and A.I. Nistor. A new approach on constant angle surface in E 3, to appear in Turkish J. Math., (2009). [6] P. Petersen. Riemannian Geometry. Graduate Texts in Mathematics, Springer Verlag, (1997). [7] J.G. Ratcliffe. Foundations of Hyperbolic Manifolds. 2-nd Edition, Graduate Texts in Mathematics, Springer (2006).